Abstract
The introduction of a format for thermoplasticity is given based on the quantities that are measurable, at least principally. The important assumption is that of equal thermoelastic behaviour within all elastic ranges. For simplicity, the theory is restricted to small deformations. A simple example is given to demonstrate the results. The question of uniqueness of the thermodynamical variables is discussed.
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References
Acharya A., Shawki T.G.: The Clausius–Duhem inequality and the structure of rate-independent plasticity. Int. J. Plast. 22(2), 229–283 (1996)
Bergander H., Luther M.: Zur Dissipation beim plastischen Fließen. Tech. Mech. 6(2), 58–65 (1985)
Bertram A.: An alternative approach to finite plasticity based on material isomorphisms. Int. J. Plast. 15(3), 353–374 (1999)
Bertram, A.: Elasticity and Plasticity of Large Deformations—An Introduction. Springer, Berlin (2005, 2008, 2012)
Bever M.G., Hold D.L., Tichener A.L.: The stored energy of cold work. Prog. Mater. Sci. 17, 1–190 (1973)
Böhlke T., Bertram A.: The evolution of Hooke’s law due to texture development in polycrystals. Int. J. Solids. Struct. 38(52), 9459–9470 (2001)
Bridgman P.W.: The thermodynamics of plastic deformation and generalized entropy. Rev. Mod. Phys. 22(1), 56–63 (1950)
Brown A.A., Casey J., Nikkel D.J.: Experiments conducted in the context of the strain-space formulation of plasticity. Int. J. Plast. 19(11), 1965–2005 (2003)
Casey J.: On elastic-thermo-plastic materials at finite deformations. Int. J. Plast. 14(1–3), 173–191 (1998)
Coleman B.D., Owen D.R.: On thermodynamics and elastic-plastic materials. Arch. Ration. Mech. Anal. 59, 25–51 (1975)
Farren W.S., Taylor G.I.: The heat developed during plastic extension of metals. Proc. R. Soc. Lon. A 107, 422–451 (1925)
Germain P., Nguyen Q.S., Suquet P.: Continuum thermodynamics. J. Appl. Mech. 50, 1010–1020 (1983)
Haupt, P.: Thermodynamics of solids. In: Muschik, W. (eds.) Non-Equilibrium Thermodynamics with Application to Solids, CISM Course, vol. 336. Springer, Wien (1993)
Houlsby G.T., Puzrin A.M.: A thermomechanical framework for constitutive models for rate-independent dissipative materials. Int. J. Plast. 16, 1017–1047 (2000)
Ikegami, K.: Experimental plasticity on the anisotropy of metals. In: Colloques internationaux du CNRS 295 Comportement mécanique de solides anisotropes, pp. 201–242 (1982)
Kamlah M., Haupt P.: On the macroscopic description of stored energy and self heating during plastic deformation. Int. J. Plast. 13(10), 893–911 (1998)
Krawietz A.: Materialtheorie. Springer, Berlin (1986)
Lehmann T.: The Constitutive Law in Thermoplasticity. CISM Course 281. Springer, Wien (1984)
Lin R.C., Brocks W., Betten J.: On dissipation inequalities and finite strain inelastic constitutive laws: theoretical and numerical comparisons. Int. J. Plast. 22, 1825–1857 (2006)
Lubliner J.: On the thermodynamic foundations of non-linear solid mechanics. Int. J. Non Linear Mech. 7, 237–254 (1972)
Lucchesi M., Silhavy M.: Thermoplastic materials with combined hardening. Int. J. Plast. 9, 291–315 (1993)
Maugin G.A.: The Thermomechanics of Plasticity and Fracture. Cambridge University Press, Cambridge (1992)
Maugin, G. A.: Thermomechanics of Nonlinear Irreversible Behaviors—An Introduction. World Sci. Singapore (1999)
Phillips A., Liu C.S., Justusson J.W.: An experimental investigation of yield surfaces at elevated temperatures. Acta Mech. 14, 119–146 (1972)
Phillips, A.: The foundations of thermoplasticity—experiments and theory. In: Zeman, J.L., Ziegler, F. (eds.) Topics in Applied Continuum Mechanics, Springer-Verlag, Wien, pp. 1–21 (1974)
Ristinmaa M., Wallin M., Ottosen N.S.: Thermodynamic format and heat generation of isotropic hardening plasticity. Acta Mech. 194, 103–121 (2007)
Rosakis P., Rosakis A.J., Ravichandran G., Hodowany J.: A thermodynamic internal variable model for the partition of plastic work into heat and stored energy in metals. J. Mech. Phys. Solids 48, 581–607 (2000)
Svendsen B.: A thermodynamic formulation of finite deformation elastoplasticity with hardening based on the concept of material isomorphism. Int. J. Plast. 14(6), 473–488 (1998)
Taylor G.I., Quinney H.: The latent heat remaining in a metal after cold working. Proc. R. Soc. Lon. A 163, 157–181 (1937)
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Bertram, A., Krawietz, A. On the introduction of thermoplasticity. Acta Mech 223, 2257–2268 (2012). https://doi.org/10.1007/s00707-012-0700-6
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DOI: https://doi.org/10.1007/s00707-012-0700-6